The prime numbers 5 p ≥ obey a pattern that can be described by two formscilitates obtaining them sequentially, being possible also to calculate the quantity of primes that are in the geometric progressions 6 1 k k + ± → ∈ as it is described in this document.
The Dirichlet's theorem (1837), initially guessed by Gauss, is a result of analytic number theory. Dirichlet, demonstrated that: For any two positive coprime integers ܽ and ܾ, there are infinite primes of the form ܽ ܾ݊, where ݊ is a non-negative integer ( ݊ ൌ 1, 2, … ). In other words, there are infinite primes which are congruent to ܽ mod b. The numbers of the form ܽ ܾ݊ is an arithmetic progression. Actually, Dirichlet checks a result somewhat more interesting than the previous claim, since he demonstrated that:Which implies that there are infinite primes, ≡ ܽ ݀݉ ܾ.The proof of the theorem uses the properties of certain Dirichlet L-functions and some results on arithmetic of complex numbers, and it is sufficiently complex that some texts about numbers theory excluded it. Here is a simple proof by reductio ad absurdum which does not require extensive mathematical knowledge.
El último teorema de Fermat (FLT), (1637), establece que, si n es un entero mayor que 2, entonces es imposible encontrar tres números naturales x, y y z donde dicha igualdad se cumple siendo (x, y)> 0 en xn + yn = zn. Este artículo muestra la metodología para probar el último teorema de Fermat por Reducción ad absurdum, el teorema de Pitágoras y la propiedad de triángulos similares, conocidos en el siglo XVII, cuando Fermat enunció el teorema.
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